ICMR* in patients under 18 years old

*ICMR - Isolated Congenital Mitral Regurgitation

Design Study Objectives

Population: N = 119 patients under 18 years old with either a CE ring implant, a Band implant or neither of those implants.

Theories:

For patients with < 26mm (small size) CE ring, there is a higher chance of relapse (which leads to re-operation/redo) caused by mitral stenosis (MS).
For patients with band, there is a higher chance of relapse caused by mitral regurgiation (MR)

Aim:

to determine whether the above are true by comparing the MS rate and the MR rate between the Band and CE ring groups in the population.
to caculate the relapse (MS or MR) probability by sex.

Methods used :

Multinomial Logistic regression
Survival analysis

Descriptive Statistics

Flow chart of the study

About the data

The data set contains variables on 119 patients. The outcome variable is Cause_of_redo (qualitative information).

3 levels
- “NONE”
- “MS”
- “MR”

The data set has a total of 45 variables (after processing). Some of the predictor variables which are going to be used in the multinomial regression model are:

Age_group, four-level categorical variable describing the age groups:
- 0-4 yrs
- 5-9 yrs
- 10-14 yrs
- 16-18 yrs
GROUP, three-level categorical variable describing the three groups of interest, patients with band, patients with CE ring and patients with neither:
- NONE
- BAND
- RING
Ring_group, three-level categorical variable describing the CE ring sub groups, patients with small size ring (<26mm), patients with large size ring (>26mm) and patients without CE ring:
- NONE
- <26mm
- \(\geq\) 26mm

Data Visualization

Multinomial Logistic Regresssion

Package used: nnet

\(\underline{Step \hspace{.05in} 1}\): Relevel the baseline groups

data$Cause_of_redo <- factor(data$Cause_of_redo, levels = c("NONE", "MR", "MS"))
data$Age_group <- factor(data$Age_group, levels = c('0-4 yrs', '5-9 yrs', '10-14 yrs', '15-18 yrs'))
data$GROUP <- factor(data$GROUP, levels = c("NONE", "BAND", "RING"))
data$Ring_Group <- factor(data$Ring_Group, levels = c("NONE", "<26", ">=26"))

\(\underline{Step \hspace{.05in} 2}\): Fit the model and obtain the results

test <- multinom(Cause_of_redo ~ Age_group + Sex + GROUP + Ring_Group, data = data)

summary(test)$coefficients

##    (Intercept) Age_group5-9 yrs Age_group10-14 yrs Age_group15-18 yrs
## MR   -22.48180         1.065216          -19.76857          -13.43422
## MS   -21.02828         1.771954          -24.99633          -15.00068
##          SexM GROUPBAND GROUPRING Ring_Group<26 Ring_Group>=26
## MR -0.5094286  20.76360  12.99527      6.434332       6.560936
## MS  0.6762916  16.64434  12.43413      7.364345       5.069786

\(\underline{Step \hspace{.05in} 3}\): Find the p-value of each coefficient

z <- summary(test)$coefficients/summary(test)$standard.errors
p <- (1 - pnorm(abs(z), 0, 1)) * 2
p

##    (Intercept) Age_group5-9 yrs Age_group10-14 yrs Age_group15-18 yrs      SexM
## MR           0       0.20761394                  0          0.9930179 0.5758157
## MS           0       0.01816458                  0          0.0000000 0.3507771
##    GROUPBAND GROUPRING Ring_Group<26 Ring_Group>=26
## MR         0         0             0   4.440892e-15
## MS         0         0             0   2.220446e-16

Comment: Overall all coefficients (except for Sex variable) are statistically significant based on their p-values being smaller 0.05. The model equation for the first row is then:

\[ \scriptsize \begin{eqnarray} \text{ln}\bigg(\frac{Pr(\text{type} = \text{MR})}{Pr(\text{type = NONE})}\bigg) &= \beta_{10} + \beta_{11}(\text{age = 5-9 yrs}) + \beta_{12}(\text{age = 10-14 yrs}) + \beta_{13}(\text{age = 15-18 yrs}) + \beta_{14}(\text{Sex = M}) \\ & + \beta_{15}(\text{grp = Band}) + \beta_{16}(\text{grp = Ring}) + \beta_{17}(\text{Ring_grp = "<26"}) + \beta_{18}(\text{Ring_grp = ">=26"}) \end{eqnarray} \]

For MR patients:

\(\beta_{15}\) The log odds of having to re-operate due to MR vs. having not to re-operate will decrease by 21.28403 if moving from GROUP = “None” to GROUP = “Band”.
\(\beta_{16}\) The log odds of having to re-operate due to MR vs. having not to re-operate will increase by 13.31299 if moving from GROUP = “None” to GROUP = “Ring”.
\(\beta_{17}\) The log odds of having to re-operate due to MR vs. having not to re-operate will increase by 6.673143 if moving from Ring_grp = “None” to Ring_grp = “<26 mm”.
\(\beta_{18}\) The log odds of having to re-operate due to MR vs. having not to re-operate will increase by 6.639843 if moving from Ring_grp = “None” to Ring_grp = “>=26 mm”.

The model equation for the second row is: \[ \scriptsize \begin{eqnarray} \text{ln}\bigg(\frac{Pr(\text{type} = \text{MS})}{Pr(\text{type = NONE})}\bigg) &= \beta_{20} + \beta_{21}(\text{age = 5-9 yrs}) + \beta_{22}(\text{age = 10-14 yrs}) + \beta_{23}(\text{age = 15-18 yrs}) + \beta_{24}(\text{Sex = M})\\ & + \beta_{25}(\text{grp = Band}) + \beta_{26}(\text{grp = Ring}) + \beta_{27}(\text{Ring_grp = "<26"}) + \beta_{28}(\text{Ring_grp = ">=26"}) \end{eqnarray} \]

For MS patients:

\(\beta_{15}\) The log odds of having to re-operate due to MS vs. having not to re-operate will decrease by 18.02806 if moving from GROUP = “None” to GROUP = “Band”.
\(\beta_{16}\) The log odds of having to re-operate due to MS vs. having not to re-operate will increase by 13.39093 if moving from GROUP = “None” to GROUP = “Ring”.
\(\beta_{17}\) The log odds of having to re-operate due to MS vs. having not to re-operate will increase by 7.736406 if moving from Ring_grp = “None” to Ring_grp = “<26 mm”.
\(\beta_{18}\) The log odds of having to re-operate due to MS vs. having not to re-operate will increase by 5.654520 if moving from Ring_grp = “None” to Ring_grp = “>=26 mm”.

For both MR and MS,

\(\beta_{11}\) & \(\beta_{21}\) The log odds of having to re-operate vs. having not to re-operate will increase if moving from age = “0-4” to age = “5-9”.
\(\beta_{12}\) & \(\beta_{22}\) The log odds of having to re-operate vs. having not to re-operate will decrease if moving from age = “0-4” to age = “10-14”.
\(\beta_{13}\) & \(\beta_{23}\) The log odds of having to re-operate vs. having not to re-operate will decreaseif moving from age = “0-4” to age = “15-18”.

Relative Risk

The ratio of the probability of choosing one outcome category over the probability of choosing the baseline category is often referred as relative risk. Relative risk can be computed by taking the exponential of the intercepts from the linear equation.

exp(coef(test))

##     (Intercept) Age_group5-9 yrs Age_group10-14 yrs Age_group15-18 yrs
## MR 1.722966e-10         2.901464       2.597890e-09       1.464176e-06
## MS 7.371118e-10         5.882338       1.393898e-11       3.056950e-07
##         SexM  GROUPBAND GROUPRING Ring_Group<26 Ring_Group>=26
## MR 0.6008388 1041156169  440324.6      622.8662       706.9329
## MS 1.9665713   16925595  251231.8     1578.6812       159.1403

The relative risk ratio switching from Age_group = 0-4 yrs to 5-9 yrs is 2.901464 for redo caused by MR vs. no redo at all.
The relative risk ratio switching from Age_group = 0-4 yrs to 10-14 yrs is 5.882338 for redo caused by MS vs. no redo at all.

Survival Analysis

Packages used:

survival
survminer

Method: Kaplan-Meier non-parametric survival estimate.

Measures of interest: time to relapse

status: censoring status 1 = censored, 2 = relapsed
sex: male = M, female = F
time: disease-free time in months

Results

Comment :

Table of survival analysis showing the first 10 observations

time	n.risk	n.event	n.censor	surv	upper	lower
9	119	0	2	1	1	1
11	117	0	1	1	1	1
14	116	0	1	1	1	1
19	115	0	1	1	1	1
21	114	0	1	1	1	1
24	113	0	1	1	1	1
26	112	1	2	0.9911	1	0.9738
27	109	1	4	0.982	1	0.9575
31	104	0	2	0.982	1	0.9575
33	102	0	1	0.982	1	0.9575

Comment:

References

n.d. Survival Analysis Basics. STHDA. http://www.sthda.com/english/wiki/survival-analysis-basics.

n.d. MULTINOMIAL LOGISTIC REGRESSION | R DATA ANALYSIS EXAMPLES. UCLA:Statistical Consulting Group. https://stats.idre.ucla.edu/r/dae/multinomial-logistic-regression/.